A noted authority (Ben Crowell) stated in a comment on What sleep quality do you get in the outdoors?
A properly pitched tarp works fine in a heavy rain. It just requires practice to set it up properly. I've sat out a very intense storm under a tarp without getting wet.
Question: How? For example: How big does it have to be? Does the tarp serve as its own ground cloth, or do you have a separate ground cloth? Will this work for a prolonged rainstorm? Will it work above timberline?
There are a few different ways to pitch a tarp. In all cases the challenge, compared to a tent which is full self supporting, is that you need to find enough anchor points to be able to pitch it with adequate tension. In fact often the exact configuration you use will be determined by what points you can find to string it up from.
A common method is to string a cord between two trees. This requires one of the knots to allow you to adjust the tension in the cord after it is tied as in this video
This line form the ridge of the tarp which is slung over it and then itself tensioned with short cords fixed to the ridge line with a prusik hitch or similar.
Then the four corners are tensioned with guy lines to ground level fixed to pegs, rocks or other trees.
The most important thing about setting it up properly is to be able to tie the proper knots easily, which comes with practice. This is what allows you to tension it properly so that it sheds water effectively and is able to resist the wind.
Tarps are most useful in forested or jungle areas where you can be sure that there will be plenty of trees to tie all the lines to and they are often used in conjunction with hammocks as in this type of terrain it is often difficult to find smooth level ground to pitch tent on and it is possible to set up a hammock and tarp camp on extremely rough and sloping ground where a tent would be impractical.
On particular advantage compared to a tent is that it is quite versatile for example it can be set up quite high and wide to provide a shelter for cooking, drying clothes or other admin during the day and then lowered to give a more enclosed space at night. Similarly, with practice and in the right terrain they can be set up and taken down quickly enough to be used for rest break in bad weather.
It is also possible to use a tarp as the basis of an improvised tent using poles carried with you or found locally. This can be a useful stop gap if there are no trees etc around but can be an awkward compromise between a proper tent and the bets use of a tarp and if you want an ultralight system you may be better off with a bivi bag, but this very much depends on the precise circumstances you are expecting.
In a lot of ways you pitch a tarp similarly to a tent.
Running ground water is an issue for both types of shelters. Many tarp users use bathtub type ground cloths which are essentially the same as tent floors. In heavy rain you want to pitch your shelter in an area with good drainage.
Tarps come in all shapes and sizes. The simplest shape is a rectangular tarp. Even the most advanced shapes do not shed wind as well as computer aided designed tents. This means it is more desirable to pitch a tarp in an area protected from the wind.
A basic flat tarp has big opening on both ends and smaller openings on the sides. For rainy conditions, you want to pitch the tarp with the sides close to the ground (especially the windward side). You also want to pitch the tarp low to minimize the openings on the ends. Ideally you want to position the tarp so the wind is not blowing through it.
You can then further protect yourself by propping your pack on the end.
One advantage of a tarp over a tent is it can made of much more waterproof material (e.g., cuben fiber) than typically used in a double walled tent. Further, condensation is less of a problem in a tarp. Finally, with a tarp you do not need to worry about the rain fly sagging and touching the tent and making it less waterproof.
